Mean-field theory of 1+1D $\mathbb{Z}_2$ lattice gauge theory with matter, by Matjaž Kebrič, Ulrich Schollwöck, Fabian Grusdt
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SciPost Physics Home Authoring Refereeing Submit a manuscript About Mean-field theory of 1+1D $\mathbb{Z}_2$ lattice gauge theory with matter Matjaž Kebrič, Ulrich Schollwöck, Fabian Grusdt SciPost Phys. 20, 017 (2026) · published 21 January 2026 doi: 10.21468/SciPostPhys.20.1.017 pdf BiBTeX RIS Submissions/Reports Abstract Lattice gauge theories (LGTs) provide valuable insights into problems in strongly correlated many-body systems. Confinement which arises when matter is coupled to gauge fields is just one of the open problems, where LGT formalism can explain the underlying mechanism. However, coupling gauge fields to dynamical charges complicates the theoretical and experimental treatment of the problem. Developing a simplified mean-field theory is thus one of the ways to gain new insights into these complicated systems. Here we develop a mean-field theory of a paradigmatic 1+1D $\mathbb{Z}_2$ lattice gauge theory with superconducting pairing term, the gauged Kitaev chain, by decoupling charge and $\mathbb{Z}_2$ fields while enforcing the Gauss law on the mean-field level. We first determine the phase diagram of the original model in the context of confinement, which allows us to identify the symmetry-protected topological transition in the Kitaev chain as a confinement transition. We then compute the phase diagram of the effective mean-field theory, which correctly captures the main features of the original LGT. This is furthermore confirmed by the Green's function results and a direct comparison of the ground state energy. This simple LGT can be implemented in state-of-the art cold atom experiments. We thus also consider string-length histograms and the electric field polarization, which are easily accessible quantities in experimental setups and show that they reliably capture the various phases. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.017TI - Mean-field theory of 1+1D $\mathbb{Z}_2$ lattice gauge theory with matterPY - 2026/01/21UR - https://scipost.org/SciPostPhys.20.1.017JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 017A1 - Kebrič, MatjažAU - Schollwöck, UlrichAU - Grusdt, FabianAB - Lattice gauge theories (LGTs) provide valuable insights into problems in strongly correlated many-body systems. Confinement which arises when matter is coupled to gauge fields is just one of the open problems, where LGT formalism can explain the underlying mechanism. However, coupling gauge fields to dynamical charges complicates the theoretical and experimental treatment of the problem. Developing a simplified mean-field theory is thus one of the ways to gain new insights into these complicated systems. Here we develop a mean-field theory of a paradigmatic 1+1D $\mathbb{Z}_2$ lattice gauge theory with superconducting pairing term, the gauged Kitaev chain, by decoupling charge and $\mathbb{Z}_2$ fields while enforcing the Gauss law on the mean-field level. We first determine the phase diagram of the original model in the context of confinement, which allows us to identify the symmetry-protected topological transition in the Kitaev chain as a confinement transition. We then compute the phase diagram of the effective mean-field theory, which correctly captures the main features of the original LGT. This is furthermore confirmed by the Green's function results and a direct comparison of the ground state energy. This simple LGT can be implemented in state-of-the art cold atom experiments. We thus also consider string-length histograms and the electric field polarization, which are easily accessible quantities in experimental setups and show that they reliably capture the various phases.ER - × @Article{10.21468/SciPostPhys.20.1.017, title={{Mean-field theory of 1+1D $\mathbb{Z}_2$ lattice gauge theory with matter}}, author={Matjaž Kebrič and Ulrich Schollwöck and Fabian Grusdt}, journal={SciPost Phys.}, volume={20}, pages={017}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.017}, url={https://scipost.org/10.21468/SciPostPhys.20.1.017},} Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 3 Matjaž Kebrič, 1 2 3 Ulrich Schollwöck, 1 2 3 Fabian Grusdt 1 Ludwig-Maximilians-Universität München / Ludwig Maximilian University of Munich [LMU] 2 Munich Center for Quantum Science and Technology [MCQST] 3 Arnold Sommerfeld Center / Arnold Sommerfeld Center for Theoretical Physics [ACS] Funders for the research work leading to this publication Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG] European Research Council [ERC] Horizon 2020 (through Organization: European Commission [EC])